Problem: Multiply the following complex numbers, marked as blue dots on the graph: $[\cos(\pi) + i \sin(\pi)] \cdot [5(\cos(\frac{1}{12}\pi) + i \sin(\frac{1}{12}\pi))]$ (Your current answer will be plotted in orange.)
Answer: Multiplying complex numbers in polar forms can be done by multiplying the lengths and adding the angles. The first number ( $\cos(\pi) + i \sin(\pi)$ ) has angle $\pi$ and radius $1$ The second number ( $5(\cos(\frac{1}{12}\pi) + i \sin(\frac{1}{12}\pi))$ ) has angle $\frac{1}{12}\pi$ and radius $5$ The radius of the result will be $1 \cdot 5$ , which is $5$ The angle of the result is $\pi + \frac{1}{12}\pi = \frac{13}{12}\pi$ The radius of the result is $5$ and the angle of the result is $\frac{13}{12}\pi$.